An iterative three-dimensional parabolic equation solver for propagation above irregular boundaries

Abstract

This paper describes the development of an iterative three-dimensional parabolic equation solver that takes into account the effects of irregular boundaries and refraction from a layered atmosphere. A terrain-following coordinate transformation, based on the well-known Beilis-Tappert mapping, is applied to the narrow-angle parabolic equation in an inhomogeneous media. The main advantage of this approach, which has been used in two dimensions in the past, is the simplification of the impedance boundary condition at the earth's surface. The transformed initialboundary value problem is discretized using the Crank-Nicholson marching scheme in the propagating direction and second-order finite-differences in the transversal plane. The proposed method relies on an efficient iterative fixedpoint solver, which involves the inversion of tridiagonal matrices only. The accuracy of the method is evaluated through a comparison with boundary element simulations in a homogeneous atmosphere above a Gaussian hill. Results show that transversal scattering occurs in the shadow zone of the obstacle where the two-dimensional parabolic equation underestimates the pressure amplitude. The model is particularly suited for the simulation of infrasound in a three-dimensional environment with realistic topographies. V

Influence of meteorological conditions and topography on the active space of mountain birds assessed by a wave-based sound propagation model

“…Note that Ostashev et al (2020) recently proposed a parabolic equation (PE) formulation that improves the inclusion of wind profiles. In addition, full 3D PE formulations (Khodr et al, 2020) have been already proposed in the literature for atmospheric sound propagation. Although they describe 3D propagation effects, they induce a large increase in the computational cost.…”

Three-dimensional topographic effects on infrasound propagation across Ascension Island

“…In the present study, a Cartesian 3DPE is used to model infrasound propagation above the Ascension Island topography (Khodr et al, 2020). The method is valid for smoothly varying terrain and lowfrequency scattering, which requires a special treatment of topographic data extracted from satellite databases.…”

“…When employing a local condition, the extension of the two-dimensional Beilis and Tappert (1979) topographic mapping to 3D is straightforward and is detailed in Khodr et al (2020). The derivation is based on the following mapping which transforms the bottom surface of the propagation domain into a flat plane,…”

“…However, volcano infrasound studies, using a more computationally expensive FDTD approach, have shown that threedimensional modelling is required to explain signal features for sources located in highly mountainous terrain Lees, 2011, 2014). Recently, a three-dimensional PE has been developed that allows for the incorporation of realistic terrain models (Khodr et al, 2020). This method is well suited to local and near-regional infrasound studies: it is computationally efficient, and provides a method for identifying and characterising topographic effects along acoustic propagation paths.…”

“…In contrast, 3D effects are significant in some cases; acoustic waves can be transversally deflected by the sides of topographic hills and mountains, leading to an increase in sound amplitude that is comparable to refraction from horizontal winds (Blom, 2020). Diffractive effects allow sound to propagate into shadow zones behind barriers, even for moderate slopes in the low scattering regime (Khodr et al, 2020).…”